I don't think he would get any naturally, since his weapon training doesn't appear to grant additional groups - it's tied to his sacred weapons instead.
However, if he could get a way to count as a fighter for the purpose of feat prerequisites (by using his warpriest bonus feats, for example), he should be able to take the Advanced Weapon Training feat.
The text says" gains weapon training as per the fighter class feature, but the benefits of his weapon training apply only to his sacred weapons".
The feat requires weapon training and a fighter level, which the archetype provides.
however as alex mack said the feat claims it affects a weapon group.
There are two possibilities here.
One you do get weapon groups and you can use their bonuses only if you get a weapon focus feat in a weapon included in the group.
Two you get the maximum weapon training bonus for all weapons you have weapon focus on.
The way I see it, One means you can grab advanced weapon training as a warpriest combat feat, but Two doesn't.
Thus I will agree with Mack that as far what was intended its option Two.
Wouldn't the sacred weapons form their own, special weapon group? Sure, it means some Advanced Weapon Training options don't work (the skills for instance) but the others should work just fine.
You could even rule that if one of your scared weapons is, for instance, a heavy blade you can get the skills for heavy blades but you'd only get them when wielding a sacred weapon that meets the second requirement (being a heavy blade).